On Wed, Dec 18, 2013 at 8:01 PM, meekerdb <meeke...@verizon.net> wrote: > On 12/18/2013 4:27 PM, Stephen Paul King wrote: > > Ever attempt to do a particular calculation with an actual infinite > dimensional Hilbert space? > > > Sure. > > > Why not? Sure, you can mod out (using symmetries and other tricks) all > of the infinite dimensions except some finite subset, > > > You can calculate all the eigenfunctions of a finite square well. > > > but that is the act that introduces the bias that I am pointing at! The > actual Hilbert spaces used to do calculi are finite dimensional. > > > Even if you only find a finite subset of eigenfunctions, the calculation > is still done in an infinite dimensional space. If you create a wave > packet it consists of infinitely many momentum eigenfunctions. I don't see > that cutting the > What else did you meant to write? > > > No, Choosing a basis and choosing a coordinate system is NOT a > convenience. You must do it. > > > Try reading Robert Wald's "Quantum Field Theory in Curved Spacetime". He > seldom chooses a coordinate system. > > I have. > > Especially in GR, where one cannot define the manifold unless there is a > choice of coordinate system on the patches of local space-time used to > define the manifold - which is then run through the diffeomorphism mill... > AFAIK, there is no global manifold that can be defined that does not > involve the requirement of stitching together of local patches of > space-time (defined per individual events) into manifolds of arbitrary > size. > > > But that doesn't require choosing a specific coordinate system, and in > fact for most manifolds it is impossible to choose a single coordinate > system. > Non sequitur > > > What must be remembered is that the "stitching operation" is very > restrictive, one cannot connect patches that have events with > different (other than an infinitesimal) values of momenta and position > associated with each. The math of GR is amazing once one is familiar with > it... > > > ?? Coordinate patches have momenta?? That's amazing all right. > that is not what I wrote. > > Brent > > -- > You received this message because you are subscribed to a topic in the > Google Groups "Everything List" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/everything-list/1NWmK1IeadI/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to email@example.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 stephe...@provensecure.com http://www.provensecure.us/ “This message (including any attachments) is intended only for the use of the individual or entity to which it is addressed, and may contain information that is non-public, proprietary, privileged, confidential and exempt from disclosure under applicable law or may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify sender immediately and delete this message immediately.” -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.